uncertainties

uncertainties allows calculations such as (2 +/- 0.1)*2 = 4 +/- 0.2 to be performed transparently. Much more complex mathematical expressions involving numbers with uncertainties can also be evaluated directly.

The uncertainties package takes the pain and complexity out of uncertainty calculations.

Detailed information about this package can be found on its main website.

Basic examples

>>> from uncertainties import ufloat

>>> x = ufloat(2, 0.25)
>>> x
2.0+/-0.25

>>> square = x**2  # Transparent calculations
>>> square
4.0+/-1.0
>>> square.nominal_value
4.0
>>> square.std_dev  # Standard deviation
1.0

>>> square - x*x
0.0  # Exactly 0: correlations taken into account

>>> from uncertainties.umath import *  # sin(), etc.
>>> sin(1+x**2)
-0.95892427466313845+/-0.2836621854632263

>>> print (2*x+1000).derivatives[x]  # Automatic calculation of derivatives
2.0

>>> from uncertainties import unumpy  # Array manipulation
>>> random_vars = unumpy.uarray([1, 2], [0.1, 0.2])
>>> print random_vars
[1.0+/-0.1 2.0+/-0.2]
>>> print random_vars.mean()
1.50+/-0.11
>>> print unumpy.cos(random_vars)
[0.540302305868+/-0.0841470984808 -0.416146836547+/-0.181859485365]

Main features

• Transparent calculations with uncertainties: no or little modification of existing code is needed. Similarly, the Python_ (or IPython) shell can be used as a powerful calculator that handles quantities with uncertainties (print statements are optional, which is convenient).
• Correlations between expressions are correctly taken into account. Thus, x-x is exactly zero, for instance (most implementations found on the web yield a non-zero uncertainty for x-x, which is incorrect).
• Almost all mathematical operations are supported, including most functions from the standard math module (sin,...). Comparison operators (>, ==, etc.) are supported too.
• Many fast operations on arrays and matrices of numbers with uncertainties are supported.
• Extensive support for printing numbers with uncertainties (including LaTeX support and pretty-printing).
• Most uncertainty calculations are performed analytically.
• This module also gives access to the derivatives of any mathematical expression (they are used by error propagation theory, and are thus automatically calculated by this module).

Installation or upgrade

To install uncertainties, use:

pip install uncertainties

To upgrade from an older version, use:

pip install --upgrade uncertainties

Further details are in the on-line documentation.

Git branches

The GitHub master branch is the latest development version. It should represent a stable pre-release and should pass the tests, but will be more experimental. Tagged releases will be available on GitHub, and correspond to the releases to PyPI. The GitHub gh-pages branch will contain a stable version of the documentation that can be viewed at <https://lmfit.github.io/uncertainties/`_. Other Github branches should be treated as unstable and in-progress development branches.

License

This package and its documentation are released under the Revised BSD License.

Voluntary donations

If you find this open-source software useful (e.g. in saving you time or helping you produce something valuable), please consider donating $10 or more.

History

This package was created back around 2009 by Eric O. LEBIGOT.

Ownership of the package was taken over by the lmfit GitHub organization in 2024.